Physical Review Letters,
Journal Year:
2018,
Volume and Issue:
121(9)
Published: Aug. 30, 2018
We
introduce
two-dimensional
topological
insulators
in
proximity
to
high-temperature
cuprate
or
iron-based
superconductors
as
platforms
of
Majorana
Kramers
pairs
zero
modes.
The
proximity-induced
pairing
at
the
helical
edge
state
insulator
serves
a
Dirac
mass,
whose
sign
changes
sample
corner
because
symmetry
high-${T}_{c}$
superconductors.
This
changing
naturally
creates
each
pair
modes
protected
by
time-reversal
symmetry.
Conceptually,
this
is
topologically
trivial
superconductor-based
approach
for
provide
quantitative
criteria
and
suggest
candidate
materials
proposal.
Reviews of Modern Physics,
Journal Year:
2019,
Volume and Issue:
91(1)
Published: March 25, 2019
The
robustness
of
the
integer
quantum
Hall
effect
electron
systems
is
due
to
existence
a
topological
invariant
that
characterizes
variation
wave
function
over
Brillouin
zone.
Topological
phenomena
are
generic
features
waves
in
periodic
media,
and
this
article
reviews
how
photonic
such
as
waveguide
arrays
metamaterials
allow
exploration
application
effects
new
physical
regimes
devices.
Reviews of Modern Physics,
Journal Year:
2021,
Volume and Issue:
93(1)
Published: Feb. 24, 2021
Quantum
systems
that
are
coupled
to
an
external
bath
can
often
be
described
in
terms
of
a
non-Hermitian
effective
Hamiltonian.
In
isolated
with
Hermitian
Hamiltonians,
topological
aspects
the
band
structure,
and
resulting
phases,
have
been
interest.
The
combination
two
concepts,
i.e.,
properties
open
systems,
leads
qualitatively
new
effects.
This
review
provides
introduction
these
quantum
mechanical
concepts
their
classical
analogs,
discusses
number
applications
ranging
from
metamaterials
dissipative
cold-atom
systems.
Advances In Physics,
Journal Year:
2020,
Volume and Issue:
69(3), P. 249 - 435
Published: July 2, 2020
A
review
is
given
on
the
foundations
and
applications
of
non-Hermitian
classical
quantum
physics.
First,
key
theorems
central
concepts
in
linear
algebra,
including
Jordan
normal
form,
biorthogonality,
exceptional
points,
pseudo-Hermiticity,
parity-time
symmetry,
are
delineated
a
pedagogical
mathematically
coherent
manner.
Building
these,
we
provide
an
overview
how
diverse
systems,
ranging
from
photonics,
mechanics,
electrical
circuits,
acoustics
to
active
matter,
can
be
used
simulate
wave
In
particular,
discuss
rich
unique
phenomena
found
therein,
such
as
unidirectional
invisibility,
enhanced
sensitivity,
topological
energy
transfer,
perfect
absorption,
single-mode
lasing,
robust
biological
transport.
We
then
explain
detail
operators
emerge
effective
description
open
systems
basis
Feshbach
projection
approach
trajectory
approach.
their
physical
relevant
variety
fields,
atomic,
molecular
optical
physics,
mesoscopic
nuclear
physics
with
emphasis
prominent
subjects
regimes,
resonances,
superradiance,
continuous
Zeno
effect,
critical
phenomena,
Dirac
spectra
chromodynamics,
nonunitary
conformal
field
theories.
Finally,
introduce
notion
band
topology
complex
present
classifications
by
providing
proof,
first
this
complete
manner,
well
number
instructive
examples.
Other
topics
related
nonreciprocal
transport,
speed
limits,
walk,
also
reviewed.
Science Advances,
Journal Year:
2018,
Volume and Issue:
4(6)
Published: June 1, 2018
Three-dimensional
topological
(crystalline)
insulators
are
materials
with
an
insulating
bulk,
but
conducting
surface
states
which
topologically
protected
by
time-reversal
(or
spatial)
symmetries.
Here,
we
extend
the
notion
of
three-dimensional
to
systems
that
host
no
gapless
states,
exhibit
hinge
states.
Their
character
is
spatio-temporal
symmetries,
present
two
cases:
(1)
Chiral
higher-order
combination
and
a
four-fold
rotation
symmetry.
chiral
modes
bulk
topology
$\mathbb{Z}_2$-classified.
(2)
Helical
mirror
come
in
Kramers
pairs
$\mathbb{Z}$-classified.
We
provide
invariants
for
both
cases.
Furthermore
show
SnTe
as
well
surface-modified
Bi$_2$TeI,
BiSe,
BiTe
helical
propose
realistic
experimental
setup
detect
In
the
presence
of
crystalline
symmetries,
certain
topological
insulators
present
a
filling
anomaly:
mismatch
between
number
electrons
in
an
energy
band
and
required
for
charge
neutrality.
this
paper,
we
show
that
anomaly
can
arise
when
corners
are
introduced
$C_n$-symmetric
with
vanishing
polarization,
having
as
consequence
existence
corner-localized
charges
quantized
multiples
$\frac{e}{n}$.
We
characterize
systematically
build
indices
relate
symmetry
representations
occupied
bands
crystal
to
quanta
fractional
robustly
localized
at
its
corners.
When
additional
chiral
is
present,
$\frac{e}{2}$
corner
accompanied
by
zero-energy
states.
application
our
atomic
fragile
discuss
role
bound
disclinations
bulk
probes
these
phases.
Physical Review Letters,
Journal Year:
2019,
Volume and Issue:
122(23)
Published: June 14, 2019
The
studies
of
topological
phases
matter
have
been
developed
from
condensed
physics
to
photonic
systems,
resulting
in
fascinating
designs
robust
devices.
Recently,
higher-order
insulators
investigated
as
a
novel
phase
beyond
the
conventional
bulk-boundary
correspondence.
Previous
mainly
focused
on
multipole
systems
with
negative
coupling
between
lattice
sites.
Here
we
experimentally
demonstrate
that
second-order
insulating
without
can
be
realized
two-dimensional
dielectric
crystals.
We
visualize
both
one-dimensional
edge
states
and
zero-dimensional
corner
by
using
near-field
scanning
technique.
Our
findings
open
new
research
frontiers
for
provide
mechanism
light
manipulating
hierarchical
way.
